As is known in the art, feedback control is one important element of modern machine design. While it is effective in most cases, physical phenomena such as static friction complicate conventional feedback control strategies such as proportional-integral-derivative (PID) control. Friction exhibits a highly-variable “hard” (discontinuous) non-linearity which challenges even advanced feedback control strategies. Other non-linearities include, but are not limited to hysteresis curves, backlash, sudden changes in an environment, non-repeatability or uncertainty in the parameter values.
Friction is everywhere. Friction and stiction exist between any two objects sliding on each other. Friction is found between valves in hydraulic pipes, between bearings and shafts, in any mechanical transmission system or in any actuator. To control motion with physical actuators, the effect of friction must be considered. In heavy industrial manipulators, friction can cause large errors in position, in some cases errors up to 50% or more in position. In precise robotic motion control, poor friction compensation leads to tracking errors. Friction compensation is thus a crucial step in designing a controller for any active system with physical actuators.
Various techniques have been proposed to compensate for friction. Generally, the approach is to establish a mathematical model of the system friction through identification procedures and then, based on this model, add a friction compensation term in the main control loop. Often, better estimation of friction can be achieved using a dynamic friction model, which is updated by a state observer in the control loop. If a model of friction is not available or cannot be identified, classical PID control with properly pre-tuned parameters may be used.
U.S. Pat. No. 6,285,913B1 describes a control system which generates a pulse train which is not dependent upon position error (open loop). The amplitude and frequency of the pulses is fixed and the amplitude of the pulse is 1-10% of the controlling range of the control signal (intentionally kept low). The pulse train is superimposed on top of a control signal going into an actuator.
One prior art reference entitled “A Simple Neuron Servo,” IEEE Transactions on Neural Networks, Vol. 2 No. 2 Mar. 1991 by Stephen P. Deweerth, et al. (hereinafter “Deweerth 1991”) describes modulation of velocity. This is achieved by a complex neural network controller whose output is a sequence of pulses. Thus, the implementation of the Deweerth system is relatively complex.
Another prior art reference entitled “Application of Electromagnetic Impulsive Force to Precise Positioning,” The Bulletin of the Japan Society of Precision Engineering, Volume 25, pp. 39-55, 1991 by Higuchi Hojjat, et al (hereinafter “Hojjat 1991”) focuses on the development of apparatus for supplying an accurate magnitude of impulse for precise positioning. The system described in this reference utilizes a main controller having an undesirable level of complexity and furthermore, the system can only modulate position.
Another prior art reference entitled “Pulse Modulation Control for Flexible Systems Under the Influence of Nonlinear Friction,” a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Washington, 2001 (hereinafter “Rathbun 2001”) describes a control scheme having an undesirable level of complexity.
It should be appreciated that the prior art techniques perform reasonably well only if some knowledge of the friction is provided. For this reason, some techniques work only for some specific problems. Hence, none of the prior art techniques are simple, robust or versatile enough to serve as a general method for friction compensation. Worse yet, if the friction is highly non-linear and/or non-repeatable none of these techniques will work consistently.
It would, therefore, be desirable to provide a method and apparatus for a simpler and more robust feedback control which copes with the non-linearities.